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Well‐balanced high‐order solver for blood flow in networks of vessels with variable properties
Author(s) -
Müller Lucas O.,
Toro Eleuterio F.
Publication year - 2013
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.2580
Subject(s) - solver , convergence (economics) , variable (mathematics) , rate of convergence , mathematics , scheme (mathematics) , flow (mathematics) , mathematical optimization , block (permutation group theory) , computer science , mathematical analysis , geometry , channel (broadcasting) , computer network , economics , economic growth
We present a well‐balanced, high‐order non‐linear numerical scheme for solving a hyperbolic system that models one‐dimensional flow in blood vessels with variable mechanical and geometrical properties along their length. Using a suitable set of test problems with exact solution, we rigorously assess the performance of the scheme. In particular, we assess the well‐balanced property and the effective order of accuracy through an empirical convergence rate study. Schemes of up to fifth order of accuracy in both space and time are implemented and assessed. The numerical methodology is then extended to realistic networks of elastic vessels and is validated against published state‐of‐the‐art numerical solutions and experimental measurements. It is envisaged that the present scheme will constitute the building block for a closed, global model for the human circulation system involving arteries, veins, capillaries and cerebrospinal fluid. Copyright © 2013 John Wiley & Sons, Ltd.